@AnnaZ, you should add your photo to the database! Your plant is the
Tree Philodendron (Thaumatophyllum bipinnatifidum) and they really can grow big like the Monstera deliciosa! Their aerial roots will sometimes reach out and encircle anything nearby but they will also grow as a stand alone plant with the aerial roots growing down and taking root to anchor the stem/base into the ground. The Tree Philo's seem to be popular landscape plants here in Florida. We had them in the yard at our house in Daytona Beach where we lived for 43 years and we have a few growing along the side of our house here in Sebastian and also on one side of the fence as a screen.
One has roots beginning to encircle a small oak tree:
I brought two potted Monstera deliciosa plants with me when we moved here 7 months ago and to show what a bad plant caretaker I can be at times ... they both were stuck out in a shady area of our yard; one is root-bound and I really need to put it in the ground or find a larger pot for it. The other one got dumped out of it's pot and it's still laying there after all these months with bare roots and only 2 leaves on a stem. It may have taken root into the ground but I haven't checked ... it's still alive though!